Abstract
We explore compactly supported scaling functions of wavelet theory by means of classical umbral calculus as reformulated by Rota and Taylor. We set a theory of orthonormal scaling umbra which leads to a very simple and elementary proof of Lawton's theorem for umbrae. When umbrae come from a wavelet setting, we recover the usual Lawton condition for the orthonormality of the integer translates of a scaling function.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have